The Toffees won at Anfield in the league for the first time this century thanks to goals from Richarlison and Gylfi Sigurdsson, but Klopp was broadly pleased with his side's efforts.
He explained: "The first goal, which we have to defend better, gave the direction of the game. It was unnecessary.
"There were plenty of good football moments so we did well from a creative point of view but we had to chase the game and were not calm enough.
"Everton defended deep and full of passion but there were still moments where we were completely free in the box but we didn't finish."
Liverpool started the second half brightly, but were unable to find an equalising goal.
And Everton secured their win with a late penalty from Sigurdsson.
Reflecting on the game, Klopp - whose team now find themselves in a fight to secure European football for next season - told Sky Sports: "In the second half, we changed formation a little because we wanted to cause them more problems. Immediately we had big chances. Sadio [Mane] twice in the box and Bobby [Firmino] was twice in promising positions, so we had all these moments.
"The penalty was late and wasn't really decisive so we don't have to talk about that too much.
"We could talk about this for an hour in detail and you would realise what you were talking about would be 90 percent positive but 10 percent was not and we have to change 10 percent because it makes the difference result wise.
"We stand here having lost 2-0. I know how important it is. We feel it deep inside. But from tomorrow on I have to use all the good stuff."